T7flavor symmetry scheme for understanding neutrino mass and mixing in 3-3-1 model with neutral leptons

We construct a new version for the 3-3-1 model based on T7flavor symmetry where the left-handed leptons under T7differ from those of our previous work while the SU (3)C⊗ SU (3)L⊗ U (1)Xgauge symmetry is retained. The flavor mixing patterns and mass splitting are obtained without perturbation. The realistic lepton mixing can be obtained if both the direction of breakings T7→Z3and Z3→{ Identity } are taken place in neutrino sector. Maximal CP violation is predicted and Cabibbo–Kobayashi–Maskawa (CKM) matrix is the identity matrix at the tree-level.

MEANING AND STRUCTURE OF HOSEA X 1-8

Hos. x 1-8 is generally seen as an accumulation of dierent prophecies composed without any coherence. A few scholars have pointed to the inclusio constituted by the key-word mizbehôt in vv. 1-2 and 8. The other verses show, however, a similar relationship. So Israel’s prosperity (v. 1a) corresponds with the despair in v. 8b, and the indictment of the kings (vv. 3-4) with their condemnation (v. 7). The calf statue is central: its derision (v. 5) and its being carried away (v. 6). So our pericope offers an example of concentric symmetry (scheme on the preceding page). This construction can help us to solve exegetical questions. So the king of v. 7 cannot be an image of the calf (vv. 5-6): in the light of the corresponding vv. 3-4, the king of v. 7 can only be the real king of Israel.

ON THE POSSIBILITY OF A SOLUTION TO THE STRONG CP-PROBLEM WITHOUT AXION IN A SU(3)H FAMILY SYMMETRY MODEL

It is shown that the 'sea-saw' model of quark mass generation within the SU (3) H gauge horizontal symmetry scheme automatically satisfies the Nelson-Barr criteria for a natural solution of the strong CP-problem if the spontaneous character of CP-violation is supposed. Some possibilities for spontaneous CP-violation are discussed.